Patent No. 8,603,574 —or "Curved touch sensor" to its friends—describes a manufacturing technique for curved touch surfaces which minimizes problems caused by substrate warping or deformation. The displays, the patent suggests, could be used in displays, touch pads, touch mice, and other... things. Apple Insider describes the technology:

To avoid deformation due to the annealing process, the patent proposes a technique that deposits a conductive thin film over a flexible substrate while it is in a flat state. Once the electrodes are in place, the substrate package is joined to a curved "forming substrate" and subsequently heated. The process results in a non-deformed curved touch sensor stackup with a thin film that benefits from the high-temperature anneal.

Some current curved touch surfaces actually use a flat substrate, with a curved glass cover to provide the apparent bend. The new technique would eliminate such cheats and, according to the patent, could produce curved touchscreens that are thinner than those that use the trick. The patent also suggests that some more weird and wonderful shapes—like waves!—could be created by applying a second or third forming substrate along the way. Useless, perhaps, but fun.

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As ever, it's important to realise that a patent merely suggests that Apple is researching these kinds of technologies, and not necessarily planning to put them into production. But with the current trend for curved displays, it seems likely that Apple is at least thinking quite hard about it—even if it doesn't plan to use it. Let's wait and see. [Apple Insider via USPTO]